Development of a New Traffic Flow Model

C.S. Putcha, J.H. Kreiner, R.R. Tadi, and M. Charoensuphong (USA)

Keywords

traffic, model, regression analysis, correlation coefficient, boundary conditions. Equation 1 shown below is a nonlinear Greenberg model [2] and does not satisfy the boundary condition at zero density, k. The equation is stated here again.

Abstract

This paper deals with development of improved and efficient traffic flow model to predict the speed of the traffic, ūs, in terms of the mean free flow speed, uf, and the density, k, in Greenberg model [2] and the result is compared using correlation coefficient r. The models proposed by Greenshields (1934) [1] and Greenberg (1959) [2] are very popular and have been in use for quite sometime. These models can be considered as classic models. The intent of this research paper is to develop an efficient and improved traffic flow model to predict the space mean speed, ūs, in terms of the mean free flow speed, uf, and the density, k. The Greenberg model [2] (which is based on fluid-flow analogy concept) satisfies the boundary condition only at jam density, kj. It violates the boundary condition at zero density, k, in the sense that it can only be attained at infinitely high speeds according to Khisty and Lall [3]. The Greenshields model [1] on the other hand gives a low correlation coefficient. The intent of this research work is to specifically arrive at an improved version of Greenberg model [2] (Putcha, Kreiner, Tadi, Manop Model). The Putcha, Kreiner, Tadi, Manop model will be accomplished by expansion of natural log expression in Greenberg expression [2] and considering only linear terms. The correlation coefficient will then be calculated. Existing experimental results [4] will be used to validate the model. These results will then be compared with the results already existing in the literature from the Greenberg model [2] as well as Greenshields model [1] and other existing models as well ([5], [6], [7], [8], and [9]). 2. Literature Review Most of the data used in the present analysis of Greenberg model [2] was obtained from Garber and Hoel [4] in the absence of elaborate field data. These experiments of Greenberg model [2] were done to improve traffic flow model to predict the speed of the traffic, ūs, in terms of the mean free flow speed, uf, and the density, k. The result will then be compared with the original Greenberg model [2], Underwood model [10] and Eddie model (11) to identify whether the Putcha, Kreiner, Tadi, Manop model is better in term of correlation coefficient r, or not. The general engineering principles used are consistent with the overall transportation objectives [12]. 3. Methodology This section describes the methodology used to improve the existing Greenberg equation. 3.1 Greenberg Model

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